[kdb+/q]: Convert adjacency matrix to adjacency list

Question

Given (rectangular) adjacency matrix m, how to construct adjacency list in q language?

In QIdioms wiki I've found solution in the k language which when run through q console with k) command gives me 'vs error:

m:(1 0 1;1 0 1)
k) (^m)_vs &,/m
'vs

Result should be:

0 0 1 1
0 2 0 2

This is what I was able to replicate in q:

k) &,/m
0 2 3 5
q) where raze m
0 2 3 5

k's^ a.k.a. shape verb is missing in q so I just did:

k) (^m)
000b
000b
q) 2 3#0b
000b
000b

Now, since:

q) parse "vs"
k) {x\:y}

I tried unsuccessfully both:

q) (2 3#0b) _vs where raze m
'
q) (2 3#0b) _\: where raze m
'type

Note that QIdioms wiki has q solution for inverse problem: from adj.list to adj.matrix.

Answer 1

You've got errors because original Q idioms are written in k2 - an old version of k which modern kdb+ version don't support. A current version of k is k4 and it's not backwards-compatible with k2.

For instance, X _vs Y where X and Y are integer atoms or lists in old k2 behaved like X vs Y will behave in kdb+ starting from 3.4t 2015.12.13: http://code.kx.com/q/ref/lists/#vs:

Since 3.4t 2015.12.13: For integer types, computes the base representation of Y in the radices X.

Another example. Indeed ^ in k2 was a shape operator, but it is not any longer. In k2 ^m would have returned 2 3 for a matrix m from your example whereas current implementation behaves like q's not null as far as I understand.

Now, back to your original question, "how to construct adjacency list in q language". One way to do it is this:

q)lm:{flip raze(til count x),''where each x}

or

k)lm:{+,/(!#x),''&:'x}

UPDATE: Here's how it works. If we were to build an adjacency list using any "verbose" language we would do something like this:

for i = 0 to <number of rows> - 1            <---- (1)
    for j = 0 to <number of columns> - 1     <---- (2)
        if M[i;j] <> 0                       <---- (3)
            print i, j

In an array language like q (1) can be "translated" into til count M because count will return the number of elements at top level, i.e. the number of rows. (2) and (3) combined can be represented by where each M. Indeed, for every row we return positions of non-zero elements. Given an original matrix m we will get:

til count m -> 0 1
where each m -> (0 2; 0 2)

All we need to do is join row and column indexes. We can't use just ,' because it will join 0 with the first 0 2 and 1 with the second 0 2 resulting in (0 0 2; 1 0 2). We need to go one level deeper, joining every element from the left with every element of every element of a nested list (0 2; 0 2) from the right, hence double apostrophes in ,''.

I hope it makes sense now.

---

Personally, I would not use flip (or + in k), I can't read an adjacency matrix in this form:

0 0 1 1
0 2 0 2

I think this is much more readable:

0 0
0 2
1 0
1 2

But it's up to you of course.